Graph Neural Networks (GNNs) have demonstrated remarkable results in various real-world applications, including drug discovery, object detection, social media analysis, recommender systems, and text classification. In contrast to their vast potential, training them on large-scale graphs presents significant computational challenges due to the resources required for their storage and processing. Graph Condensation has emerged as a promising solution to reduce these demands by learning a synthetic compact graph that preserves the essential information of the original one while maintaining the GNN's predictive performance. Despite their efficacy, current graph condensation approaches frequently rely on a computationally intensive bi-level optimization. Moreover, they fail to maintain a mapping between synthetic and original nodes, limiting the interpretability of the model's decisions. In this sense, a wide range of decomposition techniques have been applied to learn linear or multi-linear functions from graph data, offering a more transparent and less resource-intensive alternative. However, their applicability to graph condensation remains unexplored. This paper addresses this gap and proposes a novel method called Multi-view Graph Condensation via Tensor Decomposition (GCTD) to investigate to what extent such techniques can synthesize an informative smaller graph and achieve comparable downstream task performance. Extensive experiments on six real-world datasets demonstrate that GCTD effectively reduces graph size while preserving GNN performance, achieving up to a 4.0% improvement in accuracy on three out of six datasets and competitive performance on large graphs compared to existing approaches. Our code is available at https://github.com/nicolasrsantos/gctd.

How can we accurately complete tensors by learning relationships of dimensions along each mode? Tensor completion, a widely studied problem, is to predict missing entries in incomplete tensors. Tensor decomposition methods, fundamental tensor analysis tools, have been actively developed to solve tensor completion tasks. However, standard tensor decomposition models have not been designed to learn relationships of dimensions along each mode, which limits to accurate tensor completion. Also, previously developed tensor decomposition models have required prior knowledges between relations within dimensions to model the relations, expensive to obtain. This paper proposes TGL (Tensor Decomposition Learning Global and Local Structures) to accurately predict missing entries in tensors. TGL reconstructs a tensor with factor matrices which learn local structures with GNN without prior knowledges. Extensive experiments are conducted to evaluate TGL with baselines and datasets.

Hyperparameter optimization is an essential component in many data science pipelines and typically entails exhaustive time and resource-consuming computations in order to explore the combinatorial search space. Similar to this problem, other key operations in data science pipelines exhibit the exact same properties. Important examples are: neural architecture search, where the goal is to identify the best design choices for a neural network, and query cardinality estimation, where given different predicate values for a SQL query the goal is to estimate the size of the output. In this paper, we abstract away those essential components of data science pipelines and we model them as instances of tensor completion, where each variable of the search space corresponds to one mode of the tensor. Now the goal is to identify all missing entries of the tensor, corresponding to all combinations of variable values, starting from a very small sample of observed entries. In order to do so, we first conduct a thorough experimental evaluation of existing state-of-the-art tensor completion techniques. We also introduce domaininspired adaptations (such as smoothness across the discretized variable space) and an ensemble technique which is able to achieve state-of-the-art performance. We extensively evaluate existing and proposed methods in a number of generated datasets corresponding to (a) hyperparameter optimization for non-neural network models, (b) neural architecture search, and (c) variants of query cardinality estimation. By doing this, we demonstrate the effectiveness of tensor completion as a tool for automating data science pipelines. Furthermore, we release our generated datasets and code in order to provide benchmarks for future work on this topic.

Given a sparse tensor, how can we accurately capture complex latent structures inherent in the tensor while maintaining the interpretability of those structures? Tensor decomposition is a fundamental technique for analyzing tensors. Classical tensor models provide multi-linear structures that are easy to interpret, but have limitations in capturing complex structures present in real-world sparse tensors. Recent neural tensor models have extended the capabilities of classical tensor models in capturing complex structures within the data. However, this has come at the cost of interpretability: neural tensor models entangle interactions across and within latent structures in a black-box manner, making it difficult to readily understand the discovered structures. Understanding these structures, however, is crucial in applications such as healthcare, which requires transparency in critical decision-making processes.

Given a time-evolving tensor stream with missing values, how can we accurately discover latent factors in an online manner to predict missing values? Online tensor factorization is a crucial task with many important applications including the analysis of climate, network traffic, and epidemic disease. However, existing online methods have disregarded temporal locality and thus have limited accuracy.

Given a sparse time-evolving tensor, how can we effectively factorize it to accurately discover latent patterns? Tensor decomposition has been extensively utilized for analyzing various multi-dimensional real-world data. However, existing tensor decomposition models have disregarded the temporal property for tensor decomposition while most real-world data are closely related to time. Moreover, they do not address accuracy degradation due to the sparsity of time slices. The essential problems of how to exploit the temporal property for tensor decomposition and consider the sparsity of time slices remain unresolved. In this paper, we propose TATD (Time-Aware Tensor Decomposition), an accurate tensor decomposition method for sparse temporal tensors. TATD is designed to exploit time dependency and time-varying sparsity of real-world temporal tensors. We propose a new smoothing regularization with Gaussian kernel for modeling time dependency. Moreover, we improve the performance of TATD by considering time-varying sparsity. We design an alternating optimization scheme suitable for temporal tensor decomposition with our smoothing regularization. Extensive experiments show that TATD provides the state-of-the-art accuracy for decomposing temporal tensors.

Given a large tensor, how can we analyze it efficiently? Multi-dimensional arrays or tensors have been widely used to model real-world data. Tensor decomposition plays an important role in analyzing trends and major factors in tensors. While several tensor analysis tools have been developed, they show slow running time and limited scalability due to their heavy computational requirements.